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suter [353]
3 years ago
7

The probability that a single radar station will detect an enemy plane is 0.65. (a) How many such stations are required to be 98

% certain that an enemy plane flying over will be detected by at least one station?
Mathematics
1 answer:
Inga [223]3 years ago
4 0

Answer:

4 stations

Step-by-step explanation:

If we need to be at least 98% certain that an enemy plane flying over will be detected by at least one station, we must ensure that there is at most a 2% chance that no radar stations detect the plane.

The probability that a single radar station does not detect the plane is 0.35.

For n radar stations:

P=0.02=0.35^n\\n=\frac{log(0.02)}{log(0.35)}\\n=3.73

Rounding up to the next whole station, at least 4 stations are needed.

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A cylinder has a height of 7 inches and a radius of 14 inches. What is its volume? Use a
icang [17]

Answer: Volume is 4308.1 in³

Step-by-step explanation: Volume is  pii· r²·h = 3.14 · (14 in)²·7 in

3 0
2 years ago
What is the perimeter of ΔABC?
Serggg [28]

Answer:

Choice D:  Perimeter = 5 + \sqrt{65} +  \sqrt{34}  units

Step-by-step explanation:

point B(9, 2)  , point C(4, 5),  point A (1,1)

Perimeter = D( A, C)  + D (A, B)  + D (B, C)

where D (A, C) =  distance between A and C

so...

D(A, C) = root ( (4 - 1)^2 + (5 - 1)^2) = 5   from a 3-4-5 right triangle.

D(A, B) = root( (9- 1)^2 + (2 -1)^2) = root( 64 + 1) = root(65)

D(B, C) = root( (9 -4)^2 + (2 -5)^2) = root (25 + 9) = root(34)

Perimeter = 5 + root(65) + root(34)

Perimeter = 5 + \sqrt{65} +  \sqrt{34}  units

6 0
3 years ago
Find the volume of the solid formed by rotating the region bounded by the given curves about the indicated axis. Y = 1x, y = 1,
Goryan [66]

The disk method will only involve a single integral. I've attached a sketch of the bounded region (in red) and one such disk made by revolving it around the y-axis.

Such a disk has radius x = 1/y and height/thickness ∆y, so that the volume of one such disk is

π (radius) (height) = π (1/y)² ∆y = π/y² ∆y

and the volume of a stack of n such disks is

\displaystyle V_n = \sum_{i=1}^n \pi {y_i}^2 \Delta y

where y_i is a point sampled from the interval [1, 5].

As we refine the solid by adding increasingly more, increasingly thinner disks, so that ∆y converges to 0, the sum converges to a definite integral that gives the exact volume V,

\displaystyle V = \lim_{n\to\infty} V_n = \int_1^5 \frac{\pi}{y^2} \, dy

V = -\dfrac\pi y\bigg|_{y=1}^{y=5} = \boxed{\dfrac{4\pi}5}

8 0
1 year ago
Ariane borrows $300 on a 5−year loan. She is charged 5% simple interest per year. How much interest is she charged for 5 years?
AnnyKZ [126]

Answer:

Interest = $75

Total to pay back = $375

Step-by-step explanation:

The total amount she will have to pay back is found by the formula:

= Amount borrowed * (1 + rate * years)

= 300 * ( 1 + 5% * 5)

= $375

The interest is therefore:

= Amount to be paid back - Amount borrowed

= 375 - 300

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6 0
2 years ago
F(n)=x2+1<br> g(n)=2x-5<br> Find f(n)-g(n)
Artist 52 [7]
Answer:

x^2 - 2x + 6

Explanation:

(x^2 + 1) - (2x - 5)
x^2 + 1 - 2x + 5
x^2 - 2x + 6
8 0
3 years ago
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